Communications of the
Korean Mathematical Society CKMS

In this work, we establish Heisenberg-type uncertainty principle for the Bessel-Struve Fock space $\mathbb{F}_{\nu}$ associated to the Airy operator $L_{\nu}$. Next, we give an application of the theory of extremal function and reproducing kernel of Hilbert space, to establish the extremal function associated to a bounded linear operator $T:\mathbb{F}_{\nu}\rightarrow H$, where $H$ be a Hilbert space. Furthermore, we come up with some results regarding the extremal functions, when $T$ are difference operators.

Keywords: Bessel-Struve-type Fock space, Heisenberg-type uncertainty principle, extremal functions

MSC numbers: 30H20, 32A15